One must make an actual argument to persuade that this is the case, especially when considering that the world as it presents itself is that a person may choose among many options.
This is true not only in that the things that influence a person's choice are many and changing, and often subconscious that even deliberately using a simple example like we used is not completely explainable. With the coffee/tea choice for instance you may well have a subconscious influence caused by the time you picked up your coffee after forgetting about it and being unexpectedly cool now it gagged you when you took a sip. In addition to that, a legitimate influence could be that you had read the Bible and felt convicted that spending big bucks at the coffee shop was foolish and materialistic and that influenced you to choose tea the next time. What I'm saying is all these things, and I will accept self directed things, influence your choice - but the influences do in the end, determine your choice.
I am not trying here to appeal to determinism on the part of God. I am appealing to this as the reality of the makeup of ourselves as humans and I am tying it to our inclinations and proclivities as fallen humans. Richard Baxter for instance, one of my favorite Puritan writers but not a good Calvinist, said the following regarding our will, (the bolded parts are by me):
"Your will is naturally a free, that is, a self-determining faculty,
but it is viciously inclined, and backward to do good; and therefore we see, by sad experience, that it hath
not a virtuous moral freedom. But that is the wickedness of it which deserveth the punishment."
Notice that Baxter says the will is your own, and it is free and self-determining. But that it is in itself, prone to wickedness. This is where I think the Calvinists and Arminians are correct. The thing to remember in this, which even many Calvinists forget when defending Calvinism, is that
the concept of actual or potential freedom of the will is not the real issue. It is the depravity and wickedness of the actual will. The "inability" to do right is not an absolute inability but a moral inability. This is as far as I will personally go in the inability and I will not appeal to sovereignty or any type of desire by God that this be so. But I think we can be blamed.